The present disclosure relates to systems and methods for magnetic resonance imaging (“MRI”) and, more particularly, to systems and methods assessing actual gradients applied by an MRI system.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclear spins in the tissue tend to align with this polarizing field. If they are not initially aligned precisely with the polarizing field, they will precess about the field at their characteristic Larmor frequency as a top precesses about the Earth's gravitational field if the top's spin axis is not initially aligned with the field. Usually the nuclear spins are the nuclei of hydrogen atoms, but NMR active nuclei of other elements are occasionally used. At equilibrium, the individual magnetic moments of all the nuclei combine to produce a net magnetic moment Mz in the direction of the polarizing field, but the randomly oriented magnetic components in the perpendicular, or transverse, plane (x-y plane) cancel one another. If, however, the substance, or tissue, is subjected to a magnetic field (excitation field B1; also referred to as the radiofrequency (RF) field) which is in the x-y plane and which oscillates near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt, which precesses (rotates about the B0 field direction) in the x-y plane at the Larmor frequency. The typically brief application of the B1 field that accomplishes the tipping of the nuclear spins is generally known as an RF pulse. The practical value of this phenomenon resides in the signal which is emitted by the excited spins after the excitation field B1 is terminated. There is a wide variety of measurement pulse sequences (“sequences”) in which this nuclear magnetic resonance (“NMR”) phenomenon is exploited.
When utilizing these signals to produce images, the phenomenon is generally known as magnetic resonance imaging (“MRI”), and magnetic field gradients (Gx, Gy, and Gz) of the polarizing field B0 are employed. Typically, the region to be imaged experiences a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The emitted MRI signals are detected using a receiver coil. The MRI signals are then digitized and processed to reconstruct the image using one of many well-known reconstruction techniques.
Thus, the gradient system is an essential component of an MRI system. It performs spatial and temporal encoding of transverse magnetization through a spatially grading magnetic field. Gradient waveforms can be synthesized to perform a range of encoding strategies including conventional Cartesian image encoding, as well as non-Cartesian acquisitions such as radial and spiral. Despite generally being considered so, the gradient fields used for spatial encoding in clinical MRI systems are never truly linear over the imaging field-of-view (“FOV”). There are many technical factors that inevitably cause distortions in the realized gradient magnetic field, including eddy currents, mechanical/thermal vibrations, and physiologically induced magnetic fields, to name a few. These unwanted gradient distortions present an engineering challenge to realizing the actual gradient field relative to the prescribed gradient. Differences between the prescribed gradients and the actual gradients result in image artifacts, including blurriness, ringing, or phase error, to name a few.
Certain MRI techniques are more prone gradient distortions and images that suffer from gradient distortions. For example, gradient distortions can be a critical issue in non-Cartesian acquisitions, and can be further exacerbated in acquisition schemes with long readout durations, such as spiral or echo planar imaging (EPI). In these cases, the k-space trajectory is prone to deviation from the prescribed trajectory due to the accumulated error in the phase evolution of the distorted gradient. In addition, rapidly changing large gradient amplitudes generate time-varying concomitant gradients that are another source of error that distort k-space trajectory.
As such, many methods have been proposed to estimate the actual k-space trajectory. These methods can generally be classified into three major categories. A first category is frequency-encoding based methods (FEBM), where off-centered selection of a thin slice is performed to avoid signal dephasing effects caused by the gradient, followed by measurement of the phase evolution over the encoding time in the manner of frequency encoding. Although the efficacy of this measurement scheme has been verified in many critical studies, the methods suffer from limitations such as the dependency on slice selection and T2* decay. A second category is phase encoding based methods (PEBM), where the phase evolution is measured at a constant (and single) echo time after a RF pulse, which is advantageous in terms of reducing the impact of T2* decay. However, a series of RF pulses must be applied to measure the whole gradient, which limits the attainable resolution of gradient measurement that directly depends on the number of RF pulse and phase encoding time delay. The third category is external probe based methods (EPBM), extra hardware is added to the MRI system to measure the gradients at various, pre-determined positions and extrapolate the actual gradients from these measurements. That is, in EPBM, several MR field probes are deployed about the MRI system and used to record field characteristics temporally and spatially. Of course, adding additional hardware to the MRI system increases the cost and complexity of the MRI system.
Once the actual gradients are at least generally known, there are several ways to correct for the deviation of the k-space trajectory. In current generation MR systems, it is common to perform pre-emphasis correction by inputting a filtered waveform into the gradient subsystem to enable a more desirable output waveform. That is, the pre-emphasis augments the idealized, often-linear gradient signal, to pre-compensate for expected gradient variations. Gradient systems are generally characterizable as linear time invariant (LTI) systems, allowing such approaches to be used. An extension of the LTI concept utilizes a gradient impulse response function (GIRF) to deconvolve the prescribed gradient from the measured gradient. Utilizing a comprehensive calibration dataset, GIRF allows a flexible correction for gradient errors, where the distorted gradient shape can be estimated by convolving the estimated GIRF with the prescribed gradient. Even with all these efforts, reconstructed images can exhibit geometric distortion unless efforts are taken to account for gradient deviations.
Therefore, it would be desirable to have systems and methods for accurately determining actual gradients in an MRI system and using this information to improve clinical images.